Eigenvalue analysis in electromagnetic cavities using divergence free finite elements

The conventional node-based finite-element method frequently yields nonphysical solutions to the vector eigenvalue problem in electromagnetic (EM) cavities. The nonphysical modes are mainly due to inadequacy in enforcing the divergence free condition and boundary (as well as interface) conditions. The edge-based finite element method with divergence free shape functions can delete the resulting spurious solutions. This method has been used to solve various eigenvalue problems in both lossless and lossy cavities. No spurious modes are observed in the frequency range of interest. Good predictions of the lower modes are obtained in all examples. In addition to being a reliable tool for cavity mode analysis, the method also finds application in the characterization of materials when loaded in an EM cavity.